Convert physics to animation keyframe (Actions) in Blender
Here are the steps you need to follow:


Let's say you created a simulation of physics on softbody
Select your object and export the file as MDD (This will export the keyframe as data to .MDD file)
Keep the object selected, Import the .MDD file you've exported.
Now if you see the Dope sheet there should be some keyframes on it. But you cannot see anything on Action Editor. 
Remove the softbody modifier on your Object. (Hit Space, you should be able to see your simulation without the modifier)
Here is the key part, Now you have to convert the body to Rigid body to bake the keyframe to Animation(Action). Apply the rigid body modifier to the Object. 
Make the Rigid body type as Active and animated (Checkbox). (Now Hit space, you should be able to see the simulation without the object falling down, Even though you applied Rigid Body modifier)
Now, go to Object -&gt; Bake to Keyframe, I will take some time according to your mesh and simulation. But after finishing you should be able to see the keyframes on Action Editor. 
As the last step simply import the .blend file to unity.